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Abstract
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In this paper, we develop an innovative approach to study the shock wave propagation using the
Sagdeev potential method. We also present an analytical solution for Korteweg de Vries
Burgers (KdVB) and modified KdVB equation families with a generalized form of the
nonlinearity term which agrees well with the numerical one. The novelty of the current
approach is that it is based on a simple analogy of the particle in a classical potential with the
variable particle energy providing one with a deeper physical insight into the problem and can
easily be extended to more complex physical situations. We find that the current method well
describes both monotonic and oscillatory natures of the dispersive-diffusive shock structures in
different viscous fluid configurations. It is particularly important that all essential parameters of
the shock structure can be deduced directly from the Sagdeev potential in small and large potential approximation regimes. Using the new method, we find that supercnoidal waves can decay
into either compressive or rarefactive shock waves depending on the initial wave amplitude.
Current investigation provides a general platform to study a wide range of phenomena related to
nonlinear wave damping and interactions in diverse fluids including plasmas
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